# Hypothetical datalog: Complexity and expressibility

## Abstract

We present an extension of Horn-clause logic which can hypothetically add and delete tuples from a database. Such logics have been discussed in the literature, but their complexities and expressibilities have remained an open question. This paper examines two such logics in the function-free, predicate case. It is shown, in particular, that augmenting Horn-clause logic with hypothetical addition increases its data-complexity from PTIME to PSPACE. When deletions are added as well, complexity increases again, to EXPTIME. To establish expressibility, we augment the logic with *negation-by-failure* and view it as a query language for relational databases. The logic of hypothetical additions then expresses all database queries which are computable in PSPACE. When deletions are included, the logic expresses all database queries computable in EXPTIME.

## Keywords

Query Processing Predicate Symbol Database Query Polynomial Space Constant Symbol## Preview

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